Abstract
We provide two new characterizations of the Takagi function as the unique bounded solution of some systems of two functional equations. The results are independent of those obtained by Kairies (Wyż Szkoł Ped Krakow Rocznik Nauk Dydakt Prace Mat 196:73–82, 1998), Kairies (Aequ Math 53:207–241, 1997), Kairies (Aequ Math 58:183–191, 1999) and Kairies et al. (Rad Mat 4:361–374, 1989; Errata, Rad Mat 5:179–180, 1989).
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References
Kairies, H.-H.: Takagi’s function and its functional equations. Wyż. Szkoł. Ped. Krakow. Rocznik Nauk.-Dydakt. Prace Mat. 196, 73–82 (1998)
Kairies, H.-H.: Functional equations for peculiar functions. Aequ. Math. 53, 207–241 (1997)
Kairies, H.-H.: A remarkable system of eight functional equations. Aequ. Math. 58, 183–191 (1999)
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Sadowski, Ł. New characterizations of the Takagi function via functional equations. Aequat. Math. 91, 1001–1007 (2017). https://doi.org/10.1007/s00010-017-0501-z
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DOI: https://doi.org/10.1007/s00010-017-0501-z